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Episodes in the Mathematics of Medieval Islam
Vergriffenes Buch, derzeit bei uns nicht verfügbar.
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Episodes in the Mathematics of Medieval Islam - Taschenbuch

2003, ISBN: 9780387406053

[ED: Taschenbuch / Paperback], [PU: Springer, Berlin], AUSFÜHRLICHERE BESCHREIBUNG: This book presents episodes from the mathematics of medieval Islam, work which has had a great impact on the development of mathematics. The author describes the subject in its proper historical context, referring to specific Arabic texts. Among the topics discussed are decimal arithmetic, plane and spherical trigonometry, algebra, interpolation and approximation of roots of equations. This book should be of great interest to historians of mathematics, as well as to students of mathematics. The presentation is readily accessible to anyone with a background in high school mathematics. BUCHBESPRECHUNG: From the reviews: J.L. Berggren Episodes in the Mathematics of Medieval Islam "[The] first book of its kind . . . Very interesting. It is definitely the product of a skillful mathematician who has collected over the years a reasonably large number of interesting problems from medieval Arabic mathematics. None of them is pursued to exhaustion, but all of them arranged in such a way, together with accompanying exercises, so that they would engage an active mind and introduce a subject." -ZENTRALBLATT MATH "This is a most scholarly book. The presentation is in the style of a textbook each of the six chapters being followed by a set of exercises and a bibliography. ... There is a good table of contents and a comprehensive index. ... This is an excellent book full of information and thought-provoking ideas. It is worthy of careful study which will lead to a greater understanding of what the Islamic world has contributed to mathematics." (D.Stander, The Mathematical Gazette, Vol. 89 (515), 2005) "Written in 1986 and inspired by Asger Aaboe's classic Episodes in the Early History of Mathematics, this book contains a wealth of classroom-ready examples of much of the mathematics one finds in high school and early college ... . Springer has taken the right step by issuing a paperback edition to get the book into the hands of a more general readership. ... The re-issue of this gem is significant and welcomed. It will enrich your classes and deepen your perspective on mathematics and culture." (Glen van Brummelen, The MAA Mathematical Sciences Digital Library, January, 2004) INHALT: 1. Introduction.- 1. The Beginnings of Islam.- 2. Islam's Reception of Foreign Science.- 3. Four Muslim Scientists.- Al-Khw?rizm?.- Al-B?r?n?.- 'Umar al-Khayy?m?.- Al-K?sh?.- 4. The Sources.- 5. The Arabic Language and Arabic Names.- The Language.- Transliterating Arabic.- Arabic Names.- Exercises.- 2. Islamic Arithmetic.- 1. The Decimal System.- 2. K?shy?r's Arithmetic.- Survey of The Arithmetic.- Addition.- Subtraction.- Multiplication.- Division.- 3. The Discovery of Decimal Fractions.- 4. Muslim Sexagesimal Arithmetic.- History of Sexagesimals.- Sexagesimal Addition and Subtraction.- Sexagesimal Multiplication.- Multiplication by Levelling.- Multiplication Tables.- Methods of Sexagesimal Multiplication.- Sexagesimal Division.- 5. Square Roots.- Obtaining Approximate Square Roots.- Justifying the Approximation.- Justifying the Fractional Part.- Justifying the Integral Part.- 6. Al-K?sh?'s Extraction of a Fifth Root.- Laying Out the Work.- The Procedure for the First Two Digits.- Justification for the Procedure.- The Remaining Procedure.- The Fractional Part of the Root.- 7. The Islamic Dimension: Problems of Inheritance.- The First Problem of Inheritance.- The Second Problem of Inheritance.- On the Calculation of Zak?t.- Exercises.- 3. Geometrical Constructions in the Islamic World.- 1. Euclidean Constructions.- 2. Greek Sources for Islamic Geometry.- 3. Apollonios' Theory of the Conics.- Symptom of the Parabola.- Symptom of the Hyperbola.- 4. Ab? Sahl on the Regular Heptagon.- Archimedes' Construction of the Regular Heptagon.- Ab? Sahl's Analysis.- First Reduction: From Heptagon to Triangle.- Second Reduction: From Triangle to Division of Line Segment.- Third Reduction: From the Divided Line Segment to Conic Sections.- 5. The Construction of the Regular Nonagon.- Verging Constructions.- Fixed Versus Moving Geometry.- Ab? Sahl's Trisection of the Angle.- 6. Construction of the Conic Sections.- Life of Ibr?h?m b. Sin?n.- Ibr?h?m b. Sin?n on the Parabola.- Ibr?h?m b. Sin?n on the Hyperbola.- 7. The Islamic Dimension: Geometry with a Rusty Compass.- Problem 1.- Problem 2.- Problem 3.- Problem 4.- Problem 5.- Exercises.- 4. Algebra in Islam.- 1. Problems About Unknown Quantities.- 2. Sources of Islamic Algebra.- 3. Al-Khw?rizm?'s Algebra.- The Name "Algebra".- Basic Ideas in Al-Khw?rizm?'s Algebra.- Al-Khw?rizm?'s Discussion of x2 + 21 = 10x.- 4. Thabit's Demonstration for Quadratic Equations.- Preliminaries.- Th?bit's Demonstration.- 5. Ab? K?mil on Algebra.- Similarities with al-Khw?rizm?.- Advances Beyond al-Khw?rizm?.- A Problem from Ab? K?mil.- 6. Al-Karaj?'s Arithmetization of Algebra.- Al-Samaw'al on the Law of Exponents.- Al-Samaw'al on the Division of Polynomials.- The First Example.- The Second Example.- 7. 'Umar al-Khayy?m? and the Cubic Equation.- The Background to 'Umar's Work.- 'Umar's Classification of Cubic Equations.- 'Umar's Treatment of x3 + mx = n.- Preliminaries.- The Main Discussion.- 'Umar's Discussion of the Number of Roots.- 8. The Islamic Dimension: The Algebra of Legacies.- Exercises.- 5. Trigonometry in the Islamic World.- 1. Ancient Background: The Table of Chords and the Sine.- 2. The Introduction of the Six Trigonometric Functions.- 3. Abu l-Waf?'s Proof of the Addition Theorem for Sines.- 4. Nas?r al-D?n's Proof of the Sine Law.- 5. Al-B?r?n?'s Measurement of the Earth.- 6. Trigonometric Tables: Calculation and Interpolation.- 7. Auxiliary Functions.- 8. Interpolation Procedures.- Linear Interpolation.- Ibn Y?nus' Second-Order Interpolation Scheme.- 9. Al-K?sh?'s Approximation to Sin(1).- Exercises.- 6. Spherics in the Islamic World.- 1. The Ancient Background.- 2. Important Circles on the Celestial Sphere.- 3. The Rising Times of the Zodiacal Signs.- 4. Stereographic Projection and the Astrolabe.- 5. Telling Time by Sun and Stars.- 6. Spherical Trigonometry in Islam.- 7. Tables for Spherical Astronomy.- 8. The Islamic Dimension: The Direction of Pray, [SC: 0.00], Neuware, gewerbliches Angebot, H: 237mm, B: 157mm, T: 12mm, [GW: 315g]

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Episodes in the Mathematics of Medieval Islam - J.L. Berggren
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J.L. Berggren:

Episodes in the Mathematics of Medieval Islam - neues Buch

ISBN: 9780387406053

ID: 978038740605

From the reviews:The book is, in spite of the author''s more modest claims, an introductory survey of main developments in those disciplines which were particularly important in Medieval Islamic mathematics...No knowledge of mathematics (or of the history of mathematics) beyond normal high-school level is presupposed, and everything required beyond that (be it Apollonian theory of conics or the definitions of celestial circles) is explained carefully and clearly. Scattered throughout the work are a number of lucid remarks on the character of Islamic mathematics or of mathematical work in general. The book will hence not only be an excellent textbook for the teaching of the history of mathematics but also for the liberal art aspect of mathematics teaching in general.- Jens Høyrup, Mathematical Reviews...as a textbook, this work is highly commendable...It is definitely the product of a skillful mathematician who has collected over the years a reasonably large number of interesting problems from medieval Arabic mathematics. None of them is pursued to exhaustion, but all of them arranged in such a way, together with accompanying exercises, so that they would engage an active mind and introduce a subject, which I am sure the author agrees with me is, at this stage, very difficult to introduce.- G.Saliba, Zentralblatt J.L. Berggren, Books, Science and Nature, Episodes in the Mathematics of Medieval Islam Books>Science and Nature, Springer New York

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Episodes in the Mathematics of Medieval Islam - J.L. Berggren
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J.L. Berggren:
Episodes in the Mathematics of Medieval Islam - Taschenbuch

2013

ISBN: 0387406050

[SR: 1590450], Paperback, [EAN: 9780387406053], Springer, Springer, Book, [PU: Springer], 2013-10-04, Springer, This book presents episodes from the mathematics of medieval Islam, work which has had a great im...., 772030, Islam, 771714, Religious History, 65, History, 1025612, Subjects, 266239, Books, 277560, Science & Religion, 277544, Religious Studies, 58, Religion & Spirituality, 1025612, Subjects, 266239, Books, 922516, History of Mathematics, 922508, History & Philosophy, 57, Science & Nature, 1025612, Subjects, 266239, Books, 278362, History of Mathematics, 278320, Mathematics, 57, Science & Nature, 1025612, Subjects, 266239, Books, 922942, Maths, 922868, Popular Science, 57, Science & Nature, 1025612, Subjects, 266239, Books, 564352, Mathematics, 570902, Algebra, 570874, Applied Mathematics, 570912, Calculus & Mathematical Analysis, 570934, Combinatorics & Graph Theory, 570936, Geometry, 570964, Mathematical Theory, 564334, Scientific, Technical & Medical, 1025612, Subjects, 266239, Books

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Episodes in the Mathematics of Medieval Islam - Berggren, J. L.
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Berggren, J. L.:
Episodes in the Mathematics of Medieval Islam - Taschenbuch

2003, ISBN: 9780387406053

[ED: Softcover], [PU: Springer, Berlin], This book presents episodes from the mathematics of medieval Islam, work which has had a great impact on the development of mathematics. The author describes the subject in its proper historical context, referring to specific Arabic texts. Among the topics discussed are decimal arithmetic, plane and spherical trigonometry, algebra, interpolation and approximation of roots of equations. This book should be of great interest to historians of mathematics, as well as to students of mathematics. The presentation is readily accessible to anyone with a background in high school mathematics. 2003. xiv, 197 S. 18 SW-Abb. Versandfertig in 6-10 Tagen, [SC: 0.00], Neuware, gewerbliches Angebot

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Episodes in the Mathematics of Medieval Islam - J. Lennart Berggren
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J. Lennart Berggren:
Episodes in the Mathematics of Medieval Islam - Taschenbuch

2003, ISBN: 9780387406053

ID: 5661196

Softcover reprint of the original 1st ed. 1986, Softcover, Buch, [PU: Springer-Verlag New York Inc.]

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Episodes in the Mathematics of Medieval Islam
Autor:

Berggren, Lennart; Berggren, J. L.; Berggren, Len

Titel:

Episodes in the Mathematics of Medieval Islam

ISBN-Nummer:

9780387406053

This book presents episodes from the mathematics of medieval Islam, work which has had a great impact on the development of mathematics. The author describes the subject in its proper historical context, referring to specific Arabic texts. Among the topics discussed are decimal arithmetic, plane and spherical trigonometry, algebra, interpolation and approximation of roots of equations. This book should be of great interest to historians of mathematics, as well as to students of mathematics. The presentation is readily accessible to anyone with a background in high school mathematics.

Detailangaben zum Buch - Episodes in the Mathematics of Medieval Islam


EAN (ISBN-13): 9780387406053
ISBN (ISBN-10): 0387406050
Taschenbuch
Erscheinungsjahr: 2003
Herausgeber: SPRINGER VERLAG GMBH
211 Seiten
Gewicht: 0,313 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 24.05.2007 23:05:08
Buch zuletzt gefunden am 13.11.2016 18:42:34
ISBN/EAN: 9780387406053

ISBN - alternative Schreibweisen:
0-387-40605-0, 978-0-387-40605-3

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